Viscous damping in one-dimensional wave transmission

Abstract

The use of one-dimensional transmission line theory as a model for wave propagation in vascular systems is considered, particularly in relation to the damping effect of viscosity of the fluid. It is shown that the accuracy and range of validity of the theory can be increased considerably by two modifying assumptions concerning the form of the velocity profile across a vessel. If the profile is assumed to be the same as that of pulsatile flow in a rigid tube, a uniformly valid solution is obtained which embodies earlier approximations for small and large values of viscosity. If the profile is assumed to be the same as that of pulsatile flow in an elastic tube, a further improvement in the accuracy of the solution is obtained which brings the results closer to those obtained from more elaborate two-dimensional solutions. The simplicity of the one-dimensional solution is important not only as a matter of convenience but because it provides an indispensable tool for the study of wave propagation and wave reflections in arterial trees and other complex tubular structures, where two-dimensional analysis would be impractical. The two-dimensional theory is best suited to analysis in a single tube.